Basic functions and unramified local L-factors for split groups | |
Li, Wen-Wei1,2 | |
2017-05-01 | |
发表期刊 | SCIENCE CHINA-MATHEMATICS |
ISSN | 1674-7283 |
卷号 | 60期号:5页码:777-812 |
摘要 | According to a program of Braverman, Kazhdan and Ng, for a large class of split unramified reductive groups G and representations rho of the dual group Ae, the unramified local L-factor L(s, pi, rho) can be expressed as the trace of pi(f (rho,s) ) for a function f (rho,s) with non-compact support whenever Re(s) ae << 0. Such a function should have useful interpretations in terms of geometry or combinatorics, and it can be plugged into the trace formula to study certain sums of automorphic L-functions. It also fits into the conjectural framework of Schwartz spaces for reductive monoids due to Sakellaridis, who coined the term basic functions; this is supposed to lead to a generalized Tamagawa-Godement-Jacquet theory for (G, rho). In this paper, we derive some basic properties for the basic functions f (rho,s) and interpret them via invariant theory. In particular, their coefficients are interpreted as certain generalized Kostka-Foulkes polynomials defined by Panyushev. These coefficients can be encoded into a rational generating function. |
关键词 | L-function Satake isomorphism generalized Kostka-Foulkes polynomial |
DOI | 10.1007/s11425-015-0730-4 |
语种 | 英语 |
WOS研究方向 | Mathematics |
WOS类目 | Mathematics, Applied ; Mathematics |
WOS记录号 | WOS:000400086700002 |
出版者 | SCIENCE PRESS |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/25968 |
专题 | 数学所 |
通讯作者 | Li, Wen-Wei |
作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China |
推荐引用方式 GB/T 7714 | Li, Wen-Wei. Basic functions and unramified local L-factors for split groups[J]. SCIENCE CHINA-MATHEMATICS,2017,60(5):777-812. |
APA | Li, Wen-Wei.(2017).Basic functions and unramified local L-factors for split groups.SCIENCE CHINA-MATHEMATICS,60(5),777-812. |
MLA | Li, Wen-Wei."Basic functions and unramified local L-factors for split groups".SCIENCE CHINA-MATHEMATICS 60.5(2017):777-812. |
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